In what spot would the new Star Wars movie "Rogue One" go in the Machete Order?

Nowhere at all

As the originator of the Machete Order wrote after the release of Star Wars VII: The Force Awakens:

The point of Machete Order is not, and has never been, ignoring Episode I because it's bad. It's been about skipping it because it's not relevant to Luke's journey. Episodes II and III are, because we see how his father falls to the Dark Side, and we see elements of his path that are mirroring his father's.

and

Clone Wars, Episode I, Rogue Squadron, Young Han Solo, The Adventures of Yoda, Boba Fett's Big Day, and whatever other movies come out that aren't part of the numerical "Episode" structure, can all pretty much be viewed in any order, as supplemental material outside of the "main saga" which I suggest viewing in the above order. Before watching any of those movies, you just say "this takes place between X and Y" and you're done.

In other words, the Machete Order was devised to tell Luke's journey in the best possible way, without spoiling any dramatic reveals beforehand and still keeping the dramatic conclusion in place.

Rogue One is not a part of Luke's journey and is therefore not a part of the Machete Order.

The blog post I linked to has been updated to include Rogue One:

In my opinion, it doesn't matter that Rogue One takes place right before A New Hope. The purpose of Machete Order was and always will be to refocus the story of the Orig­i­nal and Prequel Trilo­gies to be about Luke's journey. Episodes II and III aren't in­cluded for all their mythos and world-build­ing, they're in­cluded because Anakin's fall is di­rectly rel­e­vant to Luke's path.

Rod Hilton, the originator of Machete Order, answered this very question in his follow-up post to Machete Order. He includes a helpful diagram as his answer to this and future questions like it:

Where Does Rogue One fit?

"Since Rogue One is basically a prequel to IV, should Machete Order start with it?"

Every time a new Star Wars movie comes out, I get a bunch of tweets and e-mails asking where it fits in Machete Order. It's flattering people care so much, but my answer is probably going to always be the same. So I'm going to try and answer it once and for all.

(modified slightly per request)

He follows the diagram with several paragraphs of justification, but essentially, his point is that, although Rogue One provides background on the events leading up to Episode IV, that movie has been beloved for 40 years without needing this additional background. As a result, it is unnecessary to the story of the original 5 "Machete Order" movies.

The plot of Rogue One is referenced directly in the opening crawl of A New Hope (Episode IV). Since Rogue One was developed as a standalone film, no prior experience with the Star Wars saga is required. So, in the new Machete order, Rogue One should be first!

I would watch Rogue One (R1) first...I feel it really sets up this "are Jedi just a hokie religion" question in ANH because there are people that obviously believe in Jedi...a city dedicated to Jedi, but until the last Vader scene the beginning of Jedi power isn't show.

Add the droids, the lead in to ANH and the demise of red 5, and it leads right in.

I'd go with the rest of the machete order to save the big Vader surprise (not so much after Luke's story), and you don't have to watch the worst rated movies until you are already quite invested in the universe/characters.

R1, IV, V, II, III, VI, VII
(8.0, 8.7, 8.8, 6.7, 7.6, 8.4, 8.1 - IMDb ratings)

I don't think Rogue One should be watched before episode 4. If Rogue One is your first Star Wars movie then its ending won't be as special/cool/nostalgic to you. It was the best part for me and that's because I had seen the other movies first. I think the best order would probably be:

4
5
1
2
3
Rogue One
6
Han Solo movie
7